It is an object of the present invention to provide an electrical power steering system for a vehicle, in which an abnormal condition of a motor current detecting device for a motor current is detected with high precision. A power steering control unit calculates a target assist torque based on a steering signal from a steering sensor and calculates a motor driving current based on such target assist torque. The control unit then calculates a difference between a motor current in a normal condition and a detected motor current, so that the difference is used as an offset correction amount. The control unit further calculates an upper and a lower limit of the offset correction amount depending on a detected temperature of the motor current detecting device. The control unit finally determines that the motor current detecting device is not in a normal condition, when the offset amount is not within a range between the upper and lower limits of the offset correction amount.